$9.$ As an incentive to attract savings deposits, most financial institutions today offer daily and even continuous compounding. This means that savings, or passbook, accounts, as well as certificates of deposit $($CDs$),$ earn interest compounded each day or even more frequently, such as every hour or even every minute. $($Continuous compounding, in which compounding occurs every instant, involves a different formula that is derived from the formula we've been using.$)$ Let's take a look at daily compounding. To calculate the compound amount, A$,$ of an investment with daily compounding, use the compound interest formula modified as follows:

Rate per period $($daily$)=$ i$/365($nominal interest rate, i$,$ divided by $365)$

Number of periods $($days$),$ n$,=$ number of days of the investment.

A $=$ P$(1+$ i$/365)$n Calculator Sequence: $(1+($ i $-$: $365))$ yx n $$ P $=$ A$.$

$($Round your answers to the nearest cent.$)$

a$)$ On April $12,$ Thomas Ash deposited $$2,600$ in a passbook savings account at $3\mathrm{.}5\%$ interest compounded daily. What is the compound amount $($in $$)$ of his account on August $5?$

b$)$ Using daily compounding, calculate the compound amount $($in $$)$ of a $$9,000$ investment for each of the three CDs$.$

The First National Bank is offering a $5$ year CD at $3\%$ interest.

The Second National Bank is offering a $5$ year CD at $4\%$ interest.

The Third National Bank has a $5$ year CD at $5\mathrm{.}5\%$ interest.

$10.$ Calculatee the present value $($principal$)$ and the compound interest $($in $$).$ Use Table $11-2.($attached$)$ Round your answers to the nearest cent.

$11.$ The following investment requires a table factor for a period beyond the table. Calculate the new table factor and the present value $($principal$).$ Use Table $11-2.$ Round your new table factor to five decimal places and your present value to the nearest cent.

$12.$ Use Table $11-2($attached$)$ to solve the problem.

The requirement for computer server capacity at a particular company is expected to increase at a rate of $15\%$ per year for the next $5$ years. If the server capacity is expected to be $1,300$ gigabytes in $5$ years, how many gigabytes of capacity are there today? Round to the nearest whole gigabyte.

$13.$Solve by using the present value formula. Round your answers $($in $$)$ to the nearest cent.